The natural convection of incompressible flow confined within an enclosed right-angled triangular and isosceles cavity was investigated numerically using the multirelaxation time lattice Boltzmann method (MRT-LBM). According to the left and inclined walls thermal boundary conditions, two cases were considered in this study. In the first case, the inclined side of the enclosure was adiabatic, and the horizontal wall was heated, while the left one was kept at a cold temperature. However, the states of the left and inclined walls were interchanged in the second case. As the flow is only transported under the convection force, this study was carried out for the Rayleigh number ranging from Ra=103 to 106. The effects of the Rayleigh number on velocity and temperature profiles, streamlines, isotherms, and average Nusselt number were investigated. The position of cold and adiabatic walls had a great effect on the results. The results obtained are in good agreement with those of the literature and show the robustness of the MRT-LBM approach. In both cases, the heat-transfer rate increases with the increase in the Rayleigh number.
A rarefied gas flow is modeled inside two cases of triangular lid-driven microcavity using single (SRT) and multi-relaxation time (MRT) lattice Boltzmann approaches. In the first one, the right angle is in the top-left corner and the upper wall moves with positive horizontal velocity. However, in the second case, the right angle is in the bottom-left corner and the bottom wall moves with negative horizontal velocity. Unlike the classical form of square cavities, widely treated in the literature, the triangular form has a diagonal wall that affects the flow motion. At the moving wall, diffuse scattering boundary condition (DSBC) is employed while at the stationary sides, a combination of bounce-back and specular reflection boundary conditions (BSBC) is used. The computations are primarily performed in the slip and early transition regimes. The rarefaction effect, given by the Knudsen number (Kn) value, on the profiles of velocity components, is examined for both approaches. This study proves that for the higher values of Kn, the SRT-LBM approach cannot provide accurate results, particularly, near the inclined wall. However, the MRT-LBM approach confirms its validity even in the transition regime. A comparison with Direct Simulation Monte Carlo (DSMC) results for horizontal velocity contours shows the efficiency of the MRT-LBM approach than the SRT-LBM one which breaks down for rarefied flows.
By using finite difference method, the problem of heat transfer and entropy generation for natural convection of a fluid inside a square cavity with inner adiabatic bodies has been investigated numerically. Calculations have been made for Rayleigh numbers ranging from 102 to 5·104 for two obstacles with different heights. Results are presented as streamlines, isotherm contours and Nusselt number for Prandtl number of 0.71 (assuming the cavity is filled with air). The obtained results demonstrate the effects of pertinent parameters on the fluid flow, thermal fields and heat transfer inside the cavity. The results show that the heat transfer rates generally increase with the shrink of the obstacle size and with the increase of Rayleigh number. The entropy generation is higher at locations with large temperature gradients. Excellent agreement is obtained with previous results in the literature.
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